{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:APZKB7J3YXU77LWDBXSZFSLK4T","short_pith_number":"pith:APZKB7J3","canonical_record":{"source":{"id":"2203.16443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.hist-ph","submitted_at":"2022-03-15T15:21:37Z","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-th"],"title_canon_sha256":"e177d69a822419eecbda895e99c8512b38064cd1c55fd017fbde129294d0e937","abstract_canon_sha256":"729f3e16fbb4812d2686b0efafa11f265ad71c895fc741cde550518a64f2ca6a"},"schema_version":"1.0"},"canonical_sha256":"03f2a0fd3bc5e9ffaec30de592c96ae4fbeeb8785423621af3a645db68b99643","source":{"kind":"arxiv","id":"2203.16443","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.16443","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"2203.16443v1","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.16443","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"APZKB7J3YXU7","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"pith_short_16","alias_value":"APZKB7J3YXU77LWD","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"pith_short_8","alias_value":"APZKB7J3","created_at":"2026-07-05T04:10:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:APZKB7J3YXU77LWDBXSZFSLK4T","target":"record","payload":{"canonical_record":{"source":{"id":"2203.16443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.hist-ph","submitted_at":"2022-03-15T15:21:37Z","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-th"],"title_canon_sha256":"e177d69a822419eecbda895e99c8512b38064cd1c55fd017fbde129294d0e937","abstract_canon_sha256":"729f3e16fbb4812d2686b0efafa11f265ad71c895fc741cde550518a64f2ca6a"},"schema_version":"1.0"},"canonical_sha256":"03f2a0fd3bc5e9ffaec30de592c96ae4fbeeb8785423621af3a645db68b99643","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:10:10.634909Z","signature_b64":"qSem3Ap6SCDtHJwgXyRIY/0/KVF++hA30QYgbzod6JVIur9JROl1XOMnbvJqYElfMK4veK4vup0N5QvzfQMBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03f2a0fd3bc5e9ffaec30de592c96ae4fbeeb8785423621af3a645db68b99643","last_reissued_at":"2026-07-05T04:10:10.634560Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:10:10.634560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.16443","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SWCW92BtmloDVHCI5J0LP98uyHEBORXHu8Cpx1D2KwAygHIb5Zg4SGdPbRUmMQYXXgpzBrcTBhzOA4wAcrNICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:11:54.030394Z"},"content_sha256":"f9a87e7b23c0cd5e011fb1f4bef40aafc2e5f0d8952cbaca46a9f4ea74076646","schema_version":"1.0","event_id":"sha256:f9a87e7b23c0cd5e011fb1f4bef40aafc2e5f0d8952cbaca46a9f4ea74076646"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:APZKB7J3YXU77LWDBXSZFSLK4T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"100 years of mathematical cosmology: Models, theories, and problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","gr-qc","hep-th"],"primary_cat":"physics.hist-ph","authors_text":"Alexander P. Yefremov, Spiros Cotsakis","submitted_at":"2022-03-15T15:21:37Z","abstract_excerpt":"An elementary survey of mathematical cosmology is presented. We cover certain key ideas and developments in a qualitative way, from the time of the Einstein static universe in 1917 until today. We divide our presentation into four main parts, the first part containing important cosmologies discovered until 1960. The second period (1960-80) contains discussions of geometric extensions of the standard cosmology, singularities, chaotic behaviour, and the initial input of particle physics ideas into cosmology. Our survey for the third period (1980-2000) continues with brief descriptions of the mai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.16443","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.16443/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vx9kVvC1SdynYxSo8D7SejfkM8i0abMiLXbAfpOaBpmUuu2xlNOWoua4ZC+U14qlve03yXoQI9FoI7VRslcoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:11:54.031012Z"},"content_sha256":"e2cdc8fa48f549fc7af86f02d1c43f9e58b0031cb156dcb963fd7cc45ecdb145","schema_version":"1.0","event_id":"sha256:e2cdc8fa48f549fc7af86f02d1c43f9e58b0031cb156dcb963fd7cc45ecdb145"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/APZKB7J3YXU77LWDBXSZFSLK4T/bundle.json","state_url":"https://pith.science/pith/APZKB7J3YXU77LWDBXSZFSLK4T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/APZKB7J3YXU77LWDBXSZFSLK4T/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T08:11:54Z","links":{"resolver":"https://pith.science/pith/APZKB7J3YXU77LWDBXSZFSLK4T","bundle":"https://pith.science/pith/APZKB7J3YXU77LWDBXSZFSLK4T/bundle.json","state":"https://pith.science/pith/APZKB7J3YXU77LWDBXSZFSLK4T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/APZKB7J3YXU77LWDBXSZFSLK4T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:APZKB7J3YXU77LWDBXSZFSLK4T","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"729f3e16fbb4812d2686b0efafa11f265ad71c895fc741cde550518a64f2ca6a","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.hist-ph","submitted_at":"2022-03-15T15:21:37Z","title_canon_sha256":"e177d69a822419eecbda895e99c8512b38064cd1c55fd017fbde129294d0e937"},"schema_version":"1.0","source":{"id":"2203.16443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.16443","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"2203.16443v1","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.16443","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"APZKB7J3YXU7","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"pith_short_16","alias_value":"APZKB7J3YXU77LWD","created_at":"2026-07-05T04:10:10Z"},{"alias_kind":"pith_short_8","alias_value":"APZKB7J3","created_at":"2026-07-05T04:10:10Z"}],"graph_snapshots":[{"event_id":"sha256:e2cdc8fa48f549fc7af86f02d1c43f9e58b0031cb156dcb963fd7cc45ecdb145","target":"graph","created_at":"2026-07-05T04:10:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.16443/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An elementary survey of mathematical cosmology is presented. We cover certain key ideas and developments in a qualitative way, from the time of the Einstein static universe in 1917 until today. We divide our presentation into four main parts, the first part containing important cosmologies discovered until 1960. The second period (1960-80) contains discussions of geometric extensions of the standard cosmology, singularities, chaotic behaviour, and the initial input of particle physics ideas into cosmology. Our survey for the third period (1980-2000) continues with brief descriptions of the mai","authors_text":"Alexander P. Yefremov, Spiros Cotsakis","cross_cats":["astro-ph.CO","gr-qc","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.hist-ph","submitted_at":"2022-03-15T15:21:37Z","title":"100 years of mathematical cosmology: Models, theories, and problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.16443","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f9a87e7b23c0cd5e011fb1f4bef40aafc2e5f0d8952cbaca46a9f4ea74076646","target":"record","created_at":"2026-07-05T04:10:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"729f3e16fbb4812d2686b0efafa11f265ad71c895fc741cde550518a64f2ca6a","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.hist-ph","submitted_at":"2022-03-15T15:21:37Z","title_canon_sha256":"e177d69a822419eecbda895e99c8512b38064cd1c55fd017fbde129294d0e937"},"schema_version":"1.0","source":{"id":"2203.16443","kind":"arxiv","version":1}},"canonical_sha256":"03f2a0fd3bc5e9ffaec30de592c96ae4fbeeb8785423621af3a645db68b99643","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03f2a0fd3bc5e9ffaec30de592c96ae4fbeeb8785423621af3a645db68b99643","first_computed_at":"2026-07-05T04:10:10.634560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:10:10.634560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qSem3Ap6SCDtHJwgXyRIY/0/KVF++hA30QYgbzod6JVIur9JROl1XOMnbvJqYElfMK4veK4vup0N5QvzfQMBCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:10:10.634909Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.16443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9a87e7b23c0cd5e011fb1f4bef40aafc2e5f0d8952cbaca46a9f4ea74076646","sha256:e2cdc8fa48f549fc7af86f02d1c43f9e58b0031cb156dcb963fd7cc45ecdb145"],"state_sha256":"bc6a81d9d7be6d23c632b5f1313948852e655189b7d1723a49d4e264d32e7177"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGeJMwZlv0pD3iPrO31N7uuyGu8ZdsLAob0INB3DuBx9P5paeSWNZFQIUq/iBxWfvcQgN9PBY0Cr2KZAfOg1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T08:11:54.034938Z","bundle_sha256":"df372e167574544dbe5c2b647f39eb5b8681260c3b7a7d2b9868490b3b81ff91"}}